Divide the following complex numbers. $ \dfrac{16+12i}{-4i}$
Answer: Since we're dividing by a single term, we can simply divide each term in the numerator separately. $ \dfrac{16+12i}{-4i} = \dfrac{16}{-4i} + \dfrac{12i}{-4i}$ Factor out a $1/i$ $\dfrac{16}{-4i} + \dfrac{12i}{-4i} = \dfrac 1i \left( \dfrac{16}{-4} + \dfrac{12i}{-4} \right) = \dfrac 1i (-4-3i)$ After simplification, $1/i$ is equal to $-i$, so we have: $\dfrac 1i (-4-3i) = -i (-4-3i) = 4i + 3i^2 = -3+4i$